Cohomological Support and the Geometric Join

Let $M,N$ be finitely generated modules over a local complete intersection $R$. Assume that all the modules $\tor^R_i(M,N)$ are zero for $i>0$. We prove that the cohomological support of $M\otimes_R N$ (in the sense of Avramov-Buchweitz) is equal to the geometric join of the cohomological supports of $M,N$. This result gives a new connection between two active areas or research, and immediately produces several interesting corollaries. Naturally, it also raises many intriguing new questions about the homological properties of modules over a complete intersection, some of which are investigated in this work. 2010 MSC Classification: 13D07

2010 Mathematics Subject Classification:

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